箭图Demazure代数I：留数下降、有限商与PBW基
Quiver Demazure algebras I: Residue descent, finite quotients, and PBW bases
- School of Mathematics and Statistics, Jiangsu Normal University（江苏师范大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过留数覆盖与根幂商研究箭图Demazure代数，建立加性及乘法PBW基，并在无箭图情形下刻画有限商的结构与单模，同时给出混合D4型族的显式计算。
AI中文摘要：
我们通过留数覆盖和根幂商研究箭图Demazure代数。由零根子系统确定的覆盖将加性代数等同于Sauter广义箭图Hecke构造的有限不动代数。她的基定理随后在任意容许留数数据和一致箭图的每个有限Weyl类型中给出加性PBW基。一个序列覆盖论证在单laced类型中给出全局乘法PBW基。在定向路径条件下，根幂商是有限维的，形式指数识别了它们的加性和乘法形式。对于无箭图，我们将混合留数商约化为有限斜群环上的矩阵代数，从余不变几何获得尖锐的非消失判据，并确定其单模。在一个混合D4型族中，我们计算了显式系数表示、维数、Loewy长度和Cartan矩阵。我们还指定了与Liu代数的直接和有限覆盖比较。
英文摘要：
We study quiver Demazure algebras through residue covers and root-power quotients. The cover determined by the zero-root subsystem identifies the additive algebra with a finite fixed algebra of Sauter's generalized quiver Hecke construction. Her basis theorem then gives additive PBW in every finite Weyl type, for arbitrary admissible residue data and uniform quivers. A sequence-cover argument gives global multiplicative PBW in simply-laced type. Under a directed-path condition, root-power quotients are finite dimensional and the formal exponential identifies their additive and multiplicative forms. For arrow-free quivers, we reduce mixed-residue quotients to matrix algebras over finite skew group rings, obtain sharp nonvanishing criteria from coinvariant geometry, and determine their simple modules. In a mixed type-$D_4$ family we compute an explicit coefficient presentation, dimensions, Loewy lengths, and Cartan matrices. We also specify the direct and finite-cover comparisons with Liu's algebras.
